A361383 a(n) is the number of locations 1..n-1 which can be reached starting from location i=a(n-1), where jumps from location i to i +- a(i) are permitted (within 1..n-1); a(1)=1. See example.

1, 1, 2, 3, 3, 4, 5, 4, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 15, 16, 15, 16, 15, 18, 17, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 22, 24, 22, 24, 23, 24, 26, 26, 26, 26, 26, 26, 26, 26, 26, 29, 32, 33, 35, 32, 35, 32, 35, 32, 35, 32, 35, 32, 36, 35, 37

Offset

1,3

Comments

For clarification: We start at the term with index a(n-1). From each term at index i, we can jump to up to two locations, which are a(i) terms away in either direction. We continue this process from the terms we have reached until we have visited all possible terms.

Links

Samuel Harkness, Table of n, a(n) for n = 1..10000

Example

We find a(8)=4 by first looking at the previous term in the sequence so far (1,1,2,3,3,4,5), which is a(7)=5. This tells us to start at location i=5. Permitted steps can reach 4 locations as follows:
  1, 1, 2, 3, 3, 4, 5
     1<-------3
  1, 1, 2, 3, 3, 4, 5
  1<-1->2
Steps from each of these locations cannot reach anything new, so a(8)=4. The reachable terms are:
  1, 1, 2, 3, 3, 4, 5
  1  1  2     3

Crossrefs

Cf. A360744, A360745, A360746, A360593, A360594, A360595, A358838.

Sequence in context: A026354 A179840 A357431 * A240153 A241435 A349320

Adjacent sequences: A361380 A361381 A361382 * A361384 A361385 A361386

Keyword

nonn

Author

Neal Gersh Tolunsky, Mar 09 2023

Extensions

More terms from Samuel Harkness, Mar 10 2023

Status

approved